A193535 Decimal expansion of log(2)/3.

2, 3, 1, 0, 4, 9, 0, 6, 0, 1, 8, 6, 6, 4, 8, 4, 3, 6, 4, 7, 2, 4, 1, 0, 7, 0, 7, 1, 5, 2, 7, 2, 5, 5, 2, 2, 6, 9, 1, 8, 3, 3, 3, 7, 8, 1, 2, 0, 0, 8, 5, 0, 8, 4, 7, 0, 6, 8, 9, 3, 3, 3, 6, 4, 9, 7, 7, 9, 7, 8, 7, 3, 9, 8, 9, 8, 9, 8, 2, 3, 8, 5, 3, 5, 2, 8, 7, 7, 7, 5, 6, 6, 5, 4, 7, 2, 8

Offset

0,1

Comments

This number is involved as an addend or subtrahend in the closed forms of certain series of reciprocals of integers (see for example A113476).

References

L. B. W. Jolley, Summation of Series, Dover (1961).

Murray R. Spiegel, Seymour Lipschutz, John Liu. Mathematical Handbook of Formulas and Tables, 3rd Ed. Schaum's Outline Series. New York: McGraw-Hill (2009): p. 135, equations 21.16 and 21.18.

Links

Table of n, a(n) for n=0..96.

Index entries for transcendental numbers

Formula

Equals lim_{n->oo} [Sum_{i = 1..n} i^2/(n^3 + i^3)]. [Jolley eq 292, p.52]

Equals Sum_{n>=1} (-1)^(n-1)/(n*2^n*binomial(2*n, n)). - Arkadiusz Wesolowski, Jan 20 2013

From Amiram Eldar, Aug 05 2020: (Start)

Equals Integral_{x=1..oo} 1/(x^4 + x) dx.

Equals Integral_{x=0..oo} 1/(exp(2*x) + 3) dx. (End)

From Peter Bala, Feb 27 2024: (Start)

Equals (1/2)*Sum_{k >= 0} (-1)^k/((3*k + 1)*(3*k + 2)) = (1/2)*(1/(2 + (1*2)^2/(18 + (4*5)^2/(2*18 + (7*8)^2/(3*18 + (10*11)^2/(4*18 + ... )))))) (continued fraction). See A052502.

Equals 7/32 + (3/2)*Sum_{k >= 0} (-1)^k/((3*k + 1)*(3*k + 2)*(3*k + 3)*(3*k + 4)*(3*k + 5)). (End)

Example

0.231049060186648...

Mathematica

RealDigits[(Log[2]/3), 10, 100][[1]]

Prog

(PARI) log(2)/3 \\ Charles R Greathouse IV, Jul 29 2011

Crossrefs

Cf. A052502, A113476.

Sequence in context: A362160 A356120 A100329 * A332645 A344855 A081247

Adjacent sequences: A193532 A193533 A193534 * A193536 A193537 A193538

Keyword

nonn,cons

Author

Alonso del Arte, Jul 29 2011

Status

approved